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HSPT Math : Concepts

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Example Questions

Example Question #22 : Geometry

Jeff decided to build a play area for his guinea pigs. The play area would be an enclosure 6 feet long, 2 feet wide, and 2 feet tall. In cubic feet, how big is the play area?

Possible Answers:

$16\ ft^{3}$

$24\ ft^{3}$

$18\ ft^{3}$

$12\ ft^{3}$

Correct answer:

$24\ ft^{3}$

Explanation:

The cubic feet of an area is found by multiping the length times the width times the height. Given that the length is six feet, the width is two feet, and that the height is two feet, the total cubic area would be found using this equation:

$length\cdot width \cdot heighth$

Here is the equation with the appropriate numbers plugged in:

$6\cdot 2\cdot 2 = 24$

Therefore, 24 cubic feet is the correct answer.

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Example Question #3 : Area Of A Rectangle Or Square

Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?

Possible Answers:

$3\ ft\times3\ ft$

$1\ ft\times12\ ft$

$3\ ft\times2\ ft$

$2\ ft\times2\ ft$

Correct answer:

$3\ ft\times2\ ft$

Explanation:

The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet.

The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer.

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Example Question #1211 : Concepts

Which of the following is equal to the area of a square with perimeter 8 meters?

Possible Answers:

$40,000 \textrm{ cm}^{2}$

$20,000 \textrm{ cm}^{2}$

$160,000 \textrm{ cm}^{2}$

$80,000 \textrm{ cm}^{2}$

Correct answer:

$40,000 \textrm{ cm}^{2}$

Explanation:

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 8, or 2, meters. One meter is equal to 100 centimeters, so the sidelength is 200 centimeters. Square this to get the area:

$200 ^{2} = 200 \times 200 = 40,000$ square centimeters.

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Example Question #1212 : Concepts

Which of the following is the area of a square with perimeter 7 feet?

Possible Answers:

$729 \textrm{ in}^{2}$

$441 \textrm{ in}^{2}$

$529 \textrm{ in}^{2}$

$961 \textrm{ in}^{2}$

Correct answer:

$441 \textrm{ in}^{2}$

Explanation:

Convert 7 feet to inches by multiplying by 12: $7 \times 12 = 84$ inches.

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 84 inches. This is $84 \div 4 = 21$ inches.

Square this to get the area:

$21 ^{2} = 21 \times 21 = 441$ square inches

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Example Question #31 : Geometry

What is the area of a square with a side length of 4?

Possible Answers:

Correct answer:

Explanation:

The area of a square is represented by the equation $\dpi{100} Area = side^{2}$ .

Therefore the area of this square is $\dpi{100} 4^{2}=16$ .

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Example Question #32 : Geometry

Square A has sides measuring 5 meters. A second square, Square B, has sides that are 2 meters longer than the sides of Square A. What is the difference in area of Square A and Square B?

Possible Answers:

$24\ m^{2}$

$49\ m^2$

$8\ m^2$

$9\ m^2$

$21\ m^2$

Correct answer:

$24\ m^{2}$

Explanation:

The area of Square A is 5 * 5, or 25 m².

Since each of Square B's sides is 2 meters longer, the sides measure 7 meters. Therefore, the area of square B is 49 m².

Subtract to find the difference in areas: $49-25=24\ m^2$

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Example Question #5 : How To Find The Area Of A Square

The ratio of the length of a side of one square to the length of the side of another square is $\frac{a}{b}$ . Give the ratio of the area of the second square to the area of the first square.

Possible Answers:

$\frac{b^2}{a}$

$\frac{a^2}{b^2}$

$\frac{b^2}{a^2}$

$\frac{b}{a^2}$

Correct answer:

$\frac{b^2}{a^2}$

Explanation:

The area of a square can be found as follows:

Area=x^2

Where:

$x=Side\ Length$

So we can write:

$\frac{Area\ 2}{Area\ 1}=\frac{b^2}{a^2}$

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Example Question #6 : How To Find The Area Of A Square

What is the area of a square if the length of one side is $\sqrt{3}$ ?

Possible Answers:

$\frac{1}{3}$

$3\sqrt{3}$

$\sqrt{3}$

Correct answer:

Explanation:

The area of a square is found by multiplying one side by itself.

$A=s\times s=s^2$

We are given the side length, allowing us to solve.

$s=\sqrt{3}$

$A=(\sqrt{3})^2=3$

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Example Question #1 : How To Find The Area Of A Trapezoid

Trapezoid

What is the area of the above trapezoid?

Possible Answers:

$142.04\textrm{ m}^{2}$

$96.48\textrm{ m}^{2}$

$218.36\textrm{ m}^{2}$

$76.32\textrm{ m}^{2}$

$109.18\textrm{ m}^{2}$

Correct answer:

$109.18\textrm{ m}^{2}$

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

$A = 0.5 \cdot (7.2 + 13.4) \cdot 10.6 =0.5 \cdot 20.6 \cdot 10.6 = 109.18\textrm{ m}^{2}$

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Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of the trapezoid:

Question_7

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid can be determined using the equation $A=\frac{1}{2}(b_1+b_2)h$ .

$A=\frac{1}{2}(6+8)(4)$

$A=\frac{1}{2}(14)(4)$

A=(7)(4)=28

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #22 : Geometry

Example Question #3 : Area Of A Rectangle Or Square

Example Question #1211 : Concepts

Example Question #1212 : Concepts

Example Question #31 : Geometry

Example Question #32 : Geometry

Example Question #5 : How To Find The Area Of A Square

Example Question #6 : How To Find The Area Of A Square

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

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